Diffraction monitoring of Rayleigh mode jets

ABSTRACT

A light diffraction technique is set forth for monitoring the behavior of small liquid jets operating in the Rayleigh mode. This monitoring enables measurement of jet parameters, and thereby further enables on-line control of these parameters.

BACKGROUND OF THE INVENTION

Particles of uniform size and shape have uses in numerous chemical andmechanical applications, especially when the shape is spherical. Forexample, toner particles for use in xerographic development systemsshould, for maximum efficiency, be as near spherical as possible anddisplay a very small size variance pattern. Toner exhibiting suchcharacteristics is also extremely useful in the testing and analysis ofxerographic-type sub-systems which act with or upon particulatematerials.

Lord Rayleigh first demonstrated that liquid jets exhibits a naturalinstability and break into segments of random length. He showed furtherthat when a periodic pressure disturbance is coupled to a small liquidjet there occurs, over a certain frequency interval, a growth of theperturbation which ultimately causes the jet to break up into uniformsegments. These segments are reshaped by surface tension into uniformlysized spheres. Optimum segment lengths or wavelength (λ) was found to berelated to the radius of the jet (a) by λ = 9a. At this wavelength thedisturbance has a maximum growth rate. Controlled breakup is possible,in principle, for all wavelengths larger than the circumference of thejets (λ > 2 π a ), but experimentally it has been found that thecondition 7a < λ < 36a must be satisfied in order to produce coherentbreakup. See, for example, J. M. Schneider, N. R. Lindblad, C. D.Hendricks, Jr., and J. M. Crowley, Journal of Applied Physics, 38, 2599(1967).

Broadly, the Rayleigh mode droplet formation technique can be seen inFIG. 1. A solution 3, consisting of the material to be sprayed,dissolved in a suitable solvent if necessary and dyed or pigment loadedas desired, is sealed under pressure in vessel 1. An opening in thevessel is covered by an aperture plate 4 which contains an array ofholes. Within the enclosure of vessel 1, and at least partiallysubmerged in solution 3, is the radiating face of an ultrasonictransducer 2.

A liquid jet of velocity V_(j) is formed at each of the apertures by thehydrostatic pressure in the vessel 1. The acoustic signal from thetransducer 2 modulates the pressure at the apertures and causes aperturbation in the jet. If the wavelength (λ) of the perturbation iswithin the limits 7a-36a, the perturbation will grow and cause the jetto break up coherently.

Each volume (π a² λ) of the jet is then converted by surface tensioninto a droplet of volume (4 π R³ /3), where R is the droplet radius.Since coherent breakup is possible over a wide range of wavelengths,without varying any other parameters the volume of the droplets obtainedcan be controlled by modifying the frequency f of the acousticperturbation, since λ = V_(j) /f.

After the solvent contained in the droplet is removed by evaporationunder the appropriate conditions, a virtually perfect solid, sphericalparticle remains. The size of the sphere thus produced depends not onlyon the size of the original liquid sphere, but also on the variousconcentration of the materials in the sprayed liquid.

Final particle size may therefore be controlled by either acousticaldrive frequency, jet velocity (vessel pressure), material concentrationsand/or aperture size. Of these controlling variables, aperture size byfar provides the greatest control range; final particle size will, ingeneral, be on the order of the size of the aperture.

After breakup of the liquid jet, an array of equal sized droplets isformed. When an array of apertures is used, the droplets will vary insize somewhat from jet to jet due to aperture size variation. However,apertures such as those existing in electro-deposited nickel screenshave a small size variation (for example, those available fromBuckbee-Mears Co., St. Paul, Minn.). Therefore, at the time of dropletformation, the droplet size distribution is quite small.

The regularity of the droplet array is eroded by air drag on theparticles; this may result in a collision between two or more particles,which in turn will cause these droplets to coalesce into new dropletswith two, three, or more times the volume of the original droplets. Thecoalesced droplets with their increased size result in a reduction inthe overall particle size uniformity.

Stroboscopic light sources and microscopes have been used in the past toobserve this breakup; however, when the jet radius becomes very small(on the order of 5μm) these observations become rather difficult. Theminimum fluid velocity necessary to form a jet increases as a ⁻ ^(1/2),and therefore if it is desired to meet the condition λ = 9a, thefrequency (f = V_(j) /λ) increases, not only as a decreases, but alsobecause the minimum workable jet velocity increases. Typically, for a5μm radius jet working at 10 meters/second, the optimum frequency is 220KHz. Most conventional stroboscopes have a maximum operating frequencyof 2500 Hz, so that it is necessary to synchronize the stroboscope on alarge subharmonic of the drive frequency. This limitation and the imagesmearing caused by the high particle velocity, small particle size, andfinite light pulse length can make observations quite difficult andconfusing. Recent wide bandwidth electro-optic modulators allowstroboscopic observations at much higher frequencies, but they requiremore complex equipment. Finally, the required microscopic observationsare difficult to make. A 5μm radius jet produces droplets on the orderof 9μm in radius; these small particles are hard to observe withtelescopic microscopes because of their low magnification. Conventionalmicroscopes with small working distances are ruled out because the spraytends to coat the objective.

An array of uniformly sized, uniformly spaced droplets such as producedby an assembly of parallel jets operating in the Rayleigh mode producesa well-known light diffraction pattern. However, it should be noted thatif the frequency of the acoustic disturbance is tuned beyond the regionwhere coherent breakup is possible, the pattern disappears abruptly. Thediffraction technique described herein greatly simplifies measurement ofall the important particle and jet parameters. It furthermore provides ameasure of overall sprayer performance, i.e., particle size uniformity.

BRIEF SUMMARY OF THE INVENTION

It is therefore an object of this invention to provide theabove-described desirable features.

It is another object of this invention to provide a relatively simplemethod for monitoring the behavior of small liquid jets operating in theRayleigh mode.

It is a further object of this invention to provide a method to controlthe breakup conditions of small liquid jets operating in the Rayleighmode.

It is a still further object of this invention to provide a method fordetermining jet malfunctions, e.g., clogging, of small jets operating inthe Rayleigh mode.

It is an even still further object of this invention to provide a methodfor selection of the optimum operating conditions of small liquid jetsoperating in the Rayleigh mode.

These and other objects are accomplished by providing a lightdiffraction technique for monitoring the behavior of small liquid jetsoperating in the Rayleigh mode. This monitoring enables measure of jetparameters and thereby further enables on-line control of theseparameters.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the invention as well as other objects andfurther features thereof, reference is made to the following detaileddisclosure of the invention taken in conjunction with the accompanyingdrawings wherein:

FIG. 1 is a partially schematic, cross-sectional view of a sprayingapparatus suitable for use with the instant invention.

FIG. 2 is a schematic representation of a diffraction pattern showingvarious characteristics thereof.

FIG. 3 is a more detailed view of the droplet formation process whichoccurs in FIG. 1.

FIG. 4 is an even more detailed schematic view of the droplets from onejet stream.

FIG. 5 is a schematic representation of an alarm system for signalingproduction of particles outside a chosen range of uniformity.

FIG. 6 is a schematic representation of a system for controlling thefrequency at which the transducer operates.

FIG. 7 is a schematic representation of a system for producing a graphicrepresentation of the diffraction pattern.

FIG. 8 is an exemplary graphical representation of a diffraction patternproduced by the system of FIG. 7.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring again to FIG. 1, the general arrangement of elements, aspartially described above, for producing the diffraction pattern can beseen. Laser 9 is directed such that its beam travels perpendicularly tothe droplet streams, through condensing lens 10 and onto screen 8 wherethe diffraction pattern is displayed.

The vertical dimension s (the breakup wavelength) is set by thefrequency of operation and jet velocity. The horizontal separation r issimply the distance between jets, which is usually taken to be periodic,but with a much longer period than that of the particles within astream. This vertical periodicity in the pattern, in the order of 2 ×10⁻ ⁵ meters, can be used to establish a diffraction pattern; adiffraction pattern which, in turn, may be used to "read" the behaviorof the spraying process.

Typical diffraction patterns are comprised of an array of dots:dotseparation in the x-direction is inversely proportional to theseparation between jets; the dot separation in the y-direction isinversely proportional to the droplet separation. Attention is nowdirected to FIG. 2 which shows an exemplary diffraction pattern of aspraying apparatus operating in the Rayleigh mode. Since the inter-jetspacing r is usually fairly large the dot separation in the x-directionis very small and often appears as a solid line(s) 14. Super-imposed onthis rectangular dot matrix there appears a circular pattern comprisingconcentric bright and dark rings, 11 and 12 respectively, the size ofwhich is inversely related to the diameter of the droplets.

Directing attention now to FIGS. 2-4 the computations for vertical dropseparation and velocity will be described. The vertical periodic patternproduces constructive interference at angles tan θ_(n) θ_(n) =nλ _(i)/s, where λ_(i) is the wavelength of the incident radiation from thelaser, θ_(n) is the angle of diffraction at the n^(th) line, and hencethe fringe separation Δx (i.e., the spacing between horizontal lines 14)on the screen at a distance d is simply Δx = λ_(i) d/s (See FIG. 4). Inpractice, Δx and d are measured, λ_(i) is known and s is determined froms= λ_(i) d/Δ x. The jet velocity is V_(j) =sf, where f is the acousticdriving frequency of transducer 2.

For a complete understanding of the technique of particle sizedetermination utilizing a circular diffraction pattern, see H. C. Van DeHulst, Light Scattering by Small Particles, J. Wiley, New York, 1962.

For the present situation it is sufficient to describe the procedure asfollows. The distance p, shown in FIG. 2, between the center of thediffraction pattern and the center of the second dark ring is measured.Also measured is the distance d between the particles and the screen onwhich the pattern is projected. Generally, this distance is taken to bethat between the condensing lens 10 shown in FIG. 1 and the screen 8,which is also the focal length of the lens. The particle radius a iscalculated from the equation: ##EQU1## Where sin θ = p/d.

Reduction in particle size uniformity causes a degradation of thediffraction pattern. This degradation is evidenced by a reduction inlight intensity contrast between light and dark rings, 11 and 12respectively in FIG. 2 and a reduction in the number of rings.

Therefore, in its most simple form, the instant invention provides forthe visual interpretation of operation parameters of a Rayleigh modespraying apparatus by diffraction pattern analysis. More intense andnumerous concentric rings produce a smaller particle size distribution.The distance between any two of the horizontal lines x is inverselyrelated to the wavelength of the jet(s), i.e., the more horizontal linesvisible, the more consistent the wavelength throughout the array.

The above technique is very convenient for monitoring the breakup of thejets and clogging of the nozzles, or for measuring the droplet diameterat the instant of formation. In general, it monitors the condition of aRayleigh sprayer very near the nozzle. However, it is also possible tomeasure the distribution of the sprayed droplets while drying, theiraverage diameter, their rate of evaporation (from their size), etc. somedistance away from the nozzle, the periodicity of the dropletarrangement is destroyed. Hence the horizontal lines as presented inFIG. 2 are absent from the diffraction pattern, but the ring pattern isstill present, and it is still true that the more uniform the particledistribution, the more intense and better defined is the diffractionpattern. The average diameter can still immediately be found from theabove expression for a, and the relative intensities of the rings allowsfor the determination of the particle size distribution.

FIGS. 5 and 6 show exemplary apparatus for accomplishing automatic orsemiautomatic control of the spraying process by electro-mechanicalmeans.

Attention is now directed to FIG. 5 wherein an alarm system forsignaling the production of particles outside a chosen range ofuniformity, i.e., and unacceptable proportion of coalesced particles, isdescribed. Photodiodes, such as those available from Hewlett Packard, 20and 21 are placed within adjoining dark and light concentric rings asshown in the drawing. Optimally, because of higher contrast ratios,photodiode 20 is in the first dark ring, and photodiode 21 is in thefirst bright ring. The outputs of the two photodiodes are amplified byamplifiers 23 and 22 respectively and the signals divided by an analogdivider 24, such as available from Function Modules, Inc., Irvin,California. The ratio of the two is fed to a comparator 25 where it iscompared to a preset (adjustable) level determined by potentiometer 26.When the ratio decreases below the minimum acceptable preset level, analarm 27 is triggered.

Potentiometer 26 sets the minimum value for the intensity differencebetween the maximum and minimum intensities shown, for example, by thefirst two rings in the pattern of FIG. 5. For purpose of illustration,the chart set forth below indicates ranges (in db.) of differences andthe corresponding per cent of singlets of standard size in the spray.

    ______________________________________                                         .5 - 1.0 db    68%                                                            1.8 - 2.75 db  75%                                                           3.2 - 5.0 db    81%                                                           4.5 - 7.5 db    85%                                                           6.5 - 9.5 db    89%                                                           10.0 - 16.0 db  95%                                                           ______________________________________                                    

This measurement can also be made after all possibility of furthercoalescence is substantially eliminated, i.e., after the particles arehardened. A convenient measurement technique is to draw the hardenedparticles in the form of a dilute aerosol through a glass-walled samplechamber through which a laser beam is directed; the diffraction patternis measured in a screen located in the opposite side of the samplechamber from the laser. An output of 75% is quite satisfactory for mostpurposes and easily obtainable from spraying apparatus operating in theRayleigh mode.

FIG. 6 is a schematic representation of an electro-mechanical apparatusfor controlling the frequency f at which ultrasonic transducer 2operates. Linear photodiode array 40, such as described by Melen inElectronics, May 24, 1973, Vol. 46, No. 11, pp. 106-111, e.g., and MOSwith an internal clock, samples the light intensity sequentially along avertical path which crosses at least two of the horizontal lines 14within the diffraction pattern. The output of this array appears as apulse train at the internal clock rate. This pulse train is smoothed bylow pass filter 42 after amplification at 41. The output of the filteris fed into a comparator 43 which has a reference set, by signal 44, ata level above the signal in the dark areas, but below the signal in thelight areas. The comparator therefore detects the bright bands andtriggers a monostable one-shot multivibrator 45. The multivibratordrives a flip-flop 46 which changes state at each bright band. Theflip-flop is reset at the end of each cycle of the diode array. Logiccontrol circuitry 48 assures that if a measurement pulse is beingprocessed at reset, it will not be passed on. This prevents errors atthe beginning and end of the array cycle.

Pulse length voltage converter 47 converts the pulse length (time) to avoltage which appears at the unit's output as a pulse (may be inhibitedby the logic). The sample and hold unit 49 is signal triggered; itsamples the height of the pulse from the converter and holds it untilthe next pulse comes along.

A low-pass filter 50 may be needed to remove unwanted noise. The outputof the sample and hold unit 49 is fed to a level shifter 52 to get thevoltage down to a level of near zero (+ or -). The frequency adjustcomponent, comprised of elements 53, 54, 55, 56 and 57 addsalgebraically the frequency set signal and the error signal. Theresulting signal is fed to the voltage controlled oscillator 2 to adjustthe output frequency.

Although the specific apparatus and process steps have been described,other elements and steps may be used where suitable.

For example, other accurate methods of "reading" the diffraction patterncan be devised. A convenient graphic representation of the particle sizedistribution can be obtained by scanning the diffraction pattern areawith a photomultiplier which is tied sequentially to a log converter anda plotter. Such an arrangement of elements is shown in FIG. 7. As inFIG. 1, the beam from laser 9 (for example, a He-Ne laser, SpectraPhysics Model 132) is directed through the array of particles 6. A beamexpander and spatial filter may be used therebetween if desired.

The light is condensed by lens 10 and the undiffracted portion thereofeliminated by stop 15 which is placed at the focal point.

A photomultiplier 16 (for example, an EMI 9558) with a small aperture(in the order of about 0.1 to about 0.2mm) scans the scattering patternin the focal plane. The output of the photomultiplier is fed into alogarithmic amplifier 17 (for example, Model 755P available from AnalogDevices). This amplifier produces a linear voltage output with accurancebetter than 1 per cent for negative current input. The output voltage isrecorded with plotter 18 which can be, for example, a Moseley 7100BStrip Chart Recorder.

The graphical output of plotter 18 is exemplified in FIG. 8. TheIntensity vs. Distance curse provides much the same information as theother methods of pattern interpretation set forth above. The maxima andminima on the graph represent, respectively, the bright and dark ringsobservable on the pattern. The graph is generally symetrical about themidline, and again, the more maxima present the more nearly the systemis operating in the preferred mode. It is not unusual for as many as15-20 maxima to appear, nor is it unusual to observe as many horizontallines.

In summary then, the following methods and operations have beendescribed for controlling a spayer operating in the Rayleigh mode:

1. Measurement of velocity and operating point,

2. Determination of optimum range of operation by brightness andsharpness of pattern,

3. Feedback systems to control pressure or frequency or indicatemalfunctions (absence of acoustic signal, insufficient amplitude, etc.),and

4. Scan nozzle to determine zones not operating adequately.

It will be understood that various changes in details, materials, stepsand arrangements of parts, which have herein been described andillustrated in order to explain the nature of the invention, will occurto and, may be made by those skilled in the art upon a reading of thedisclosure within the principle scope of the invention.

What is claimed is:
 1. A method for monitoring the behavior of jetsproducing streams of droplets by operating in the Rayleigh mode,comprising:a. intercepting in the proximity of said jets said streams ofdroplets with coherent radiation, λ₁, said radiation being directedorthogonal to the direction of travel of said stream of droplets,wherein said radiation is diffracted into a pattern of concentric,alternating light and dark rings superimposed upon at least one pair ofdark bands; and b. intercepting said pattern upon a screen at adistance, d, from said streams; said pattern being characterized by thedistance between the dark bands ΔX = λ₁ d/s where s is the separationbetween individual droplets in a stream of droplets and by the distancefrom the center of the concentric bands to the middle of the second darkring p where the droplet radius a = 7.016 ÷ p/d.
 2. The method of claim1 further including the steps of:c. intercepting said streams ofdroplets with said coherent radiation at a location sufficiently remotefrom the jets to form another diffraction pattern lacking said pair ofdark bands; d. calculating the droplet radius at the remote location;and e. comparing the droplet radius at the remote location to thedroplet radius in the proximity of said jets to determine drying rate ofsaid droplets.
 3. A method for monitoring separation, s, betweenindividual droplets in a stream of droplets produced by a jet operatingin the Rayleigh mode, comprising:a. intercepting in the proximity ofsaid jet said stream of droplets with coherent radiation, λ₁, saidradiation being directed orthogonal to the direction of travel of saidstream of droplets, wherein said radiation is diffracted into a patternof concentric, alternating light and dark rings superimposed upon atleast one pair of dark bands; b. intercepting said pattern upon a screenat a distance, d, from said stream wherein the distance between the darkbands of the intercepted pattern ΔX = λ₁ d/s; and c. monitoring ΔX forindication of any change in the value of s.
 4. The method of claim 3wherein the separation, s, between individual droplets in each of aplurality of streams is monitored by scanning the coherent radiation. 5.A method for determining the velocity, V_(j), of a stream of dropletsproduced by a jet operating in the Rayleigh mode at a frequency f,comprising:a. intercepting in the proximity of said jet said stream ofdroplets with coherent radiation, λ₁, said radiation being directedorthogonal to the direction of travel of said stream of droplets,wherein said radiation is diffracted into a pattern of concentric,alternating light and dark rings superimposed upon at least one pair ofdark bands; b. intercepting said pattern upon a screen at a distance d,from said stream wherein the distance between the dark bands of theintercepted pattern, ΔX = λ₁ d/s, where s is the separation distancebetween individual droplets in said stream of droplets; c. measuring ΔXand determining s = λ₁ d/ X; and d. determining V_(j) by obtaining theproduct of s and f.
 6. The method of claim 5 wherein the velocity V_(j)for each of a plurality of streams is determined by scanning thecoherent radiation.